Dynamics Are Expensive

Dynamics Are Expensive

If geometry is cheap, what is expensive? The answer came from the Lenia evolution series (V11–V12): dynamics. Specifically, the capacity to increase integration under threat — to become more unified when the world becomes more hostile.

Naive patterns decompose under stress ($\Delta\intinfo = -6.2\%$). So do LLMs. So do randomly initialized agents. Geometry is present everywhere; the biological signature — integration rising under threat — is rare. The Lenia series tracked what produces it:

1. Homogeneous evolution (V11.1): Selection pressure alone is insufficient ($-6.0\%$).
2. Heterogeneous chemistry (V11.2): Diverse viability manifolds produce a +2.1pp shift.
3. Curriculum training (V11.7): Graduated stress exposure is the only intervention that improves novel-stress generalization.
4. Evolvable attention (V12): State-dependent interaction topology produces $\intinfo$ increase in 42% of evolutionary cycles — the largest single-intervention effect — but robustness stabilizes near 1.0 without further improvement.

Attention is necessary but not sufficient. The system reaches an integration threshold without crossing it.